Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
484 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#951 | C2 | semidirect |
| 3. C2×#909 | C2 | semidirect |
| 4. C2×#887 | C2 | semidirect |
| 5. C3×#417 | C2 | semidirect |
| 6. #5118 | C2 | semidirect |
| 7. #4966 | C2 | semidirect |
| 8. #4798 | C2 | semidirect |
| 9. #4795 | C2 | semidirect |
| 10. #4767 | C2 | semidirect |
| 11. #4762 | C2 | semidirect |
| 56. #417 | D3 | semidirect |
| 77. C2×Dic6 | D4 | semidirect |
| 242. Dic3 | #137 | semidirect |
| 308. C3 | #3037 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5832 | 2 |
| C2×#951 | 2 |
| C2×#909 | 2 |
| C2×#887 | 2 |
| C3×#417 | 2 |
| #5118 | 2 |
| #4966 | 2 |
| #4798 | 2 |
| #4795 | 2 |
| #4767 | 2 |
| #4762 | 2 |
| #3037 | 3 |